Mathematics in Ancient and Medieval India c6.s9.27

c6.s9.27

(b) *The area of a triangle:* The theorems relating to the areas are found in Euclid (c. 300 B. C.) and apparently were common property long before his time. Egyptian surveyors, even before the time of Euclid were in the habit of finding the areas of the triangular and rectangular fields. Indians too, were able to calculate the area of a triangle (=½), rectangle (=length) and isosceles trapezium [=½ (sum of the parallel sides) × distance between the parallel sides] in connection with the construction of altars on the ground.⁵ The same formulae are also found in the works of Āryabhaṭa I¹. (c. 499 A. D.), and others². For area of the scalene triangle³ Bhāskara I (c. 600 A. D.) perhaps knew the area of a triangle with sides a, b and c to be √(s(s-a)(s-b)(s-c)) where 2s = a + b + c. This formula may be obtained in terms of the sides as follows :